*** Q1: Is it possible to move/reorganize these Forums, placing them into newly created categories? ***
In your control panel under forum settings there should be a drop down box for each forum under the column "Category". You should be able to put a forum into any category you have created.
*** Q2:Is there a limit to the number of categories I can include on my site. ***
I don't think there is a limit on the amount of categories you can make.
*** Q3: As a site administrator, is it possible to move a user's "Post" into another Forum or Category? ***
Yes, you can move posts. Currently in the 6.x series you have to goto each post that you want to move and at the bottom of the page there are your admin functions [ Close Topic, Move Topic, and Delete Topic ].